Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-8x+4y &= 4 \\ -2x-3y &= -6\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-2x = 3y-6$ Divide both sides by $-2$ to isolate $x$ $x = {-\dfrac{3}{2}y + 3}$ Substitute this expression for $x$ in the first equation. $-8({-\dfrac{3}{2}y + 3}) + 4y = 4$ $12y - 24 + 4y = 4$ Simplify by combining terms, then solve for $y$ $16y - 24 = 4$ $16y = 28$ $y = \dfrac{7}{4}$ Substitute $\dfrac{7}{4}$ for $y$ in the top equation. $-8x+4( \dfrac{7}{4}) = 4$ $-8x+7 = 4$ $-8x = -3$ $x = \dfrac{3}{8}$ The solution is $\enspace x = \dfrac{3}{8}, \enspace y = \dfrac{7}{4}$.